Modular anomaly equations in N=2* theories and their large-N limit

Understand

We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background.

• We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed.
• In this regime instantons are not suppressed.
• We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law.